wezterm has support for both implicit and explicit hyperlinks.

Implicit hyperlinks are produced by running a series of rules over the output displayed in the terminal to produce a hyperlink. There is a default rule to match URLs and make them clickable, but you can also specify your own rules to make your own links. As an example, at my place of work many of our internal tools use T123 to indicate task number 123 in our internal task tracking system. It is desirable to make this clickable, and that can be done with the following configuration in your ~/.wezterm.lua:

return {
  hyperlink_rules = {
    -- Linkify things that look like URLs and the host has a TLD name.
    -- Compiled-in default. Used if you don't specify any hyperlink_rules.
    {
      regex = '\\b\\w+://[\\w.-]+\\.[a-z]{2,15}\\S*\\b',
      format = '$0',
    },

    -- linkify email addresses
    -- Compiled-in default. Used if you don't specify any hyperlink_rules.
    {
      regex = [[\b\w+@[\w-]+(\.[\w-]+)+\b]],
      format = 'mailto:$0',
    },

    -- file:// URI
    -- Compiled-in default. Used if you don't specify any hyperlink_rules.
    {
      regex = [[\bfile://\S*\b]],
      format = '$0',
    },

    -- Linkify things that look like URLs with numeric addresses as hosts.
    -- E.g. http://127.0.0.1:8000 for a local development server,
    -- or http://192.168.1.1 for the web interface of many routers.
    {
      regex = [[\b\w+://(?:[\d]{1,3}\.){3}[\d]{1,3}\S*\b]],
      format = '$0',
    },

    -- Make task numbers clickable
    -- The first matched regex group is captured in $1.
    {
      regex = [[\b[tT](\d+)\b]],
      format = 'https://example.com/tasks/?t=$1',
    },

    -- Make username/project paths clickable. This implies paths like the following are for GitHub.
    -- ( "nvim-treesitter/nvim-treesitter" | wbthomason/packer.nvim | wez/wezterm | "wez/wezterm.git" )
    -- As long as a full URL hyperlink regex exists above this it should not match a full URL to
    -- GitHub or GitLab / BitBucket (i.e. https://gitlab.com/user/project.git is still a whole clickable URL)
    {
      regex = [[["]?([\w\d]{1}[-\w\d]+)(/){1}([-\w\d\.]+)["]?]],
      format = 'https://www.github.com/$1/$3',
    },
  },
}

Note that it is generally convenient to use literal strings ([[...]]) when declaring your hyperlink rules, so you won't have to escape backslashes. In the example above, all cases except the first use literal strings for their regular expressions.

wezterm supports the relatively new Hyperlinks in Terminal Emulators specification that allows emitting text that can be clicked and resolve to a specific URL, without the URL being part of the display text. This allows for a cleaner presentation.

The gist of it is that running the following bash one-liner:

printf '\e]8;;http://example.com\e\\This is a link\e]8;;\e\\\n'

will output the text This is a link that when clicked will open http://example.com in your browser.